The non-linear autonomous Wei–Norman equations are equivalent to a linear system of non-autonomous equations on a Lie group and in some cases provide a method to find the solution. In case of all classical simple Lie groups, they can be reduced to a hierarchy of matrix Riccati equations. This is achieved by an appropriate choice of generators of the Lie algebra and of the order of their exponentials in the solution provided by the Wei–Norman method. The unitary case, of particular significance for quantum optimal-control problems, fits into this scheme by considering the complexification of the unitary group and its Lie algebra sl(|N;|C). The result cannot be extended to all simple Lie algebras, in particular to the exceptional algebra g₂.